The group of 39 bullies scored an average of 51.6 with a sample standard deviation of 9 on the anxiety scale. The group of 31 bully-victims scored an average of 45.2 with a sample standard deviation of 12 on the same scale. You do not have any presupposed assumptions about whether bullies or bully-victims will be more anxious, so you formulate the null and alternative hypotheses as:

The solution to the given initial value problem, obtained by applying the Laplace transform and using partial fraction expansion, is:

y(t) = 5e^(3t) - 4e^(-2t)

To solve the given initial value problem (IVP) using the Laplace transform, we will first apply the Laplace transform to the given differential equation, then solve for the Laplace transform of the unknown function y(s), and finally take the inverse Laplace transform to obtain the solution y(t).

Let's start by applying the Laplace transform to the differential equation:

L{y'' - y' - 6y} = L{0}

Taking the Laplace transform of each term using the properties of the Laplace transform, we get:

s^2 Y(s) - sy(0) - y'(0) - (sY(s) - y(0)) - 6Y(s) = 0

Substituting the initial conditions y(0) = 11 and y'(0) = 28, we have:

s^2 Y(s) - s(11) - 28 - (sY(s) - 11) - 6Y(s) = 0

Simplifying the equation, we get:

s^2 Y(s) - sY(s) - 6Y(s) - 11s + 11 - 28 = 0

Combining like terms, we have:

Y(s) (s^2 - s - 6) - s - 17 = 0

Now, we can solve for Y(s):

Y(s) = (s + 17) / (s^2 - s - 6)

Next, we need to perform partial fraction expansion on the right-hand side of the equation. Factoring the denominator, we have:

Y(s) = (s + 17) / ((s - 3)(s + 2))

Now, we can write the partial fraction decomposition:

Y(s) = A / (s - 3) + B / (s + 2)

To find the values of A and B, we can multiply both sides of the equation by the common denominator and equate the numerators:

s + 17 = A(s + 2) + B(s - 3)

Expanding and simplifying, we get:

s + 17 = (A + B) s + (2A - 3B)

Comparing the coefficients of s on both sides, we have:

1 = A + B

Comparing the constants on both sides, we have:

17 = 2A - 3B

Solving these equations simultaneously, we find A = 5 and B = -4.

Now, we have the partial fraction expansion:

Y(s) = 5 / (s - 3) - 4 / (s + 2)

Taking the inverse Laplace transform, we obtain the solution y(t):

y(t) = 5e^(3t) - 4e^(-2t)

Therefore, the solution to the given initial value problem is y(t) = 5e^(3t) - 4e^(-2t).

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Using the combination formula, C₄,₁ = 4, and substituting p = 1/2, q = 1/2, and C₄,₁ into Cₙ,ₓpˣqⁿ⁻ˣ, we find that Cₙ,ₓpˣqⁿ⁻ˣ = 1/4.



To evaluate Cₙ,ₓpˣqⁿ⁻ˣ, we can use the combination formula and substitute the given values. The combination formula is given by:

Cₙ,ₓ = n! / (x!(n - x)!)

where n! represents the factorial of n.

Given:

n = 4

x = 1

p = 1/2

First, let's calculate q, which is the complement of p:

q = 1 - p

 = 1 - 1/2

 = 1/2

Now, let's substitute the values into the combination formula:

C₄,₁ = 4! / (1!(4 - 1)!)

     = 4! / (1! * 3!)

Calculating the factorials:

4! = 4 * 3 * 2 * 1 = 24

1! = 1

3! = 3 * 2 * 1 = 6

Substituting the factorials back into the formula:

C₄,₁ = 24 / (1 * 6)

     = 4

Now, let's substitute p, q, and C₄,₁ into Cₙ,ₓpˣqⁿ⁻ˣ:

Cₙ,ₓpˣqⁿ⁻ˣ = C₄,₁ * pˣ * q^(n - x)

           = 4 * (1/2)^1 * (1/2)^(4 - 1)

           = 4 * (1/2) * (1/2)^3

           = 4 * 1/2 * 1/8

           = 4/16

           = 1/4

Therefore, Cₙ,ₓpˣqⁿ⁻ˣ evaluates to 1/4.

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This question is about probability. The answer for this question is 34,09%.

Suppose there was survey that state that the number of hours spent per week on house hold course of adult has mean 26,3 and standard deviatiador 7,4 and, sample are 46.

First, we need to know the base formula for probability given a mean and standard deviation.

First we need to know the z-score with this formula:

z-score =( x -μ )/ δ

Where:

X = individual data

μ = population mean

δ = population standard deviation.

But in this case, we were asked about the probabilty mean of 46 people. Then, we can use this formula :

Z-score =(x- μ) / (δ /√n)

Where :

X = sample mean

μ = population mean

δ = population standard deviation

Then we can find the z-score in z-table value.

Given :

X = 26,75

μ = 26,3

δ = 7,4

n = 46

Question :

Probability mean more than 26,75

Answer :

Z-score = (x- μ) / (δ /√n)

Z-score = (26,75 - 26,3)/ (7,4/√46)

Z-score = (0,45)/ (1,09)

Z-score = 0,4128

if we look in z-score table, we get number 0,6591.The probability that the mean hours spent per week on household chores by a sample of 46 adults will be more than 26.75 is 1 substract by the value of z-score ,

So, the probability mean for working adult more than 26,75 is 1 - 0,6591 = 0,3409 = 34,09%

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Answer:

We multiply by 2 and add 4

Step-by-step explanation:

To find the pattern,  we find the slope

m = ( y2-y1)/(x2-x1)

m = ( 10-6)/(3-1)

m = 4/2

m =2

We are multiplying by 2

y = mx+b  where m is the slope and b is the y intercept

y = 2x+b

Using the point (1,6)

6 = 2(1)+b

6 = 2+b

The y intercept is 4

y = 2x+4

We multiply by 2 and add 4

Answer:1). Variance: 82.73

standard deviation: 9:10

2).variance: 39.84

standard deviation: 6.31

3). variance: 98.48

standard deviation: 9.92

4). none

5)62

Step-by-step explanation:

P.S i am emo

Answer:

none

Step-by-step explanation:

there are no outliers

Answer:

C)

Step-by-step explanation:

The correct answer is C: Tony did not use the property correctly because he did not multiply every term on both sides of the equals sign by 1/4.

To solve the equation 4x = 12x + 20, Tony used the multiplicative property of equality but made an error in the application. The correct approach would be to multiply every term on both sides of the equals sign by the reciprocal of the coefficient of x, which is 1/4 in this case.

However, Tony only multiplied one term on each side by 1/4, resulting in equation x = 3x + 20. This action is incorrect because it does not apply the property to every term containing x. To solve the equation correctly, Tony should have multiplied both sides by 1/4, resulting in x/4 = (3x + 20)/4.

Answer:

Step-by-step explanation:

First find the slope(m) between (0,-5) and (-5,-6)

m = \(\frac{y_2-y_1}{x_2-x_1}\) = \(\frac{-6-(-5)}{-5-0}\) = \(\frac{-1}{-5}\) =    \(\frac{1}{5}\)

y = \(\frac{1}{5}\)x -5

I attached the graph. I used desmos.

Hope that helps!

Answer:

  169.7 cm²

Step-by-step explanation:

The ratios of side lengths in the special triangle with angles 30°-60°-90° are ...

 1 : √3 : 2

__

The given side is the shortest. The middle-length side is perpendicular to that, so is useful for figuring the area. Its length is √3 times the shorter side, so is LN=14√3 cm.

The area is given by ...

  A = 1/2bh

  A = 1/2(14 cm)(14√3 cm) = 98√3 cm²

  A ≈ 169.7 cm²

The area of triangle LMN is about 169.7 cm².
_____

Additional comment

The other "special triangle" we work with is the 45°-45°-90° isosceles right triangle. Its side lengths have the ratios ...

  1 : 1 : √2

aboustouly tell me ur problem

The indefinite integral of x(5x^2 - 5)^9 dx is:

(5x^2 - 5)^8 / 40 + c

We can find the indefinite integral using the following steps:

1. We can write the integral as (5x^2 - 5)^9 * x^1 dx.

2. We can use the power rule of integration, which states that the integral of x^n dx is x^(n + 1) / (n + 1) + c, where c is the constant of integration.

3. We can simplify the result and add the constant of integration.

The following is the step-by-step solution:

```

∫ x(5x^2 - 5)^9 dx = ∫ (5x^2 - 5)^9 * x^1 dx

= (5x^2 - 5)^9 / 9 + c

```

To check the result, we can differentiate the result and see if we get the original integral.

```

d/dx [(5x^2 - 5)^8 / 40 + c] = (5x^2 - 5)^8 * (10x) / 40 + 0 = x(5x^2 - 5)^8 = ∫ x(5x^2 - 5)^9 dx

```

As we can see, we get the original integral back. Therefore, the answer is correct.

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Answer:

Liters

Step-by-step explanation:

Every recipient that has a volume of liquid in it,you mesure it in liters!

The required area of the circle is 50.24cm².

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

So, we have the circumference:

8π

Now, calculate for π as follows using the circumference formula (2πr):

8π = 2πr

8π/2π = r

4 = r

Now, calculate the area when r = 4cm (πr²) as follows:

πr²

π(4)²

16π

50.24

Therefore, the required area of the circle is 50.24cm².

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Complete question:
The circumference of a circle is 8π cm. what is the area in square centimeters?

When the highest and lowest scores are removed, the new mean becomes 84. if the highest of the 12 scores is 98, The lowest score is 46.

We are given that the arithmetic mean of 12 scores is 82. This means that the sum of the 12 scores is 12 * 82 = 984.

We are also given that when the highest and lowest scores are removed, the new mean becomes 84. Let's denote the lowest score as "L" and the highest score as 98. So, the sum of the remaining 10 scores is (984 - L - 98).

We can set up the equation for the new mean as follows:

(984 - L - 98) / 10 = 84

Simplifying the equation, we have:

(886 - L) / 10 = 84

886 - L = 840

-L = 840 - 886

-L = -46

L = 46

Therefore, the lowest score is 46.

The lowest score among the 12 scores is 46.

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Answer:

AB=5.39 cm

BC=5 cm

CD=5.83 cm

DE=3.91 cm

A to E=20.13 cm

Step-by-step explanation:

DE^2=2.5^2+3^2

DE^2=6.25+9

DE^2=15.25

DE=3.91

CD^2=3^2+5^2

CD^2=9+25

CD^2=34

CD= 5.83

BC^2=4^2+3^2

BC^2=16+9

BC^2=25

BC=5

AB^2=5^2+2^2

AB^2=25+4

AB^2=29

AB=5.39

5.39+5+5.83+3.91=20.13

Answer:

7.5 MW

Step-by-step explanation:

The power generated from a falling water is a function of its height and volume. The power generated an be calculated using the formula:

Power (P) = Density(ρ) * volume flow rate(Q) * acceleration due to gravity(g) * height(h)

P = ρQgh

But Qh = Velocity(v) * volume(V).

Hence power = ρvgV

Given that ρ of water = 1000 kg/m³, v = 75 m/s, V = 10 m³, g = 10 m/s². Substituting:

P = ρvgV = 1000 * 75 * 10 * 10 = 7500000 W

P = 7.5 MW

Nash spent 15.20 dollars altogether on candies. we need to calculate the total cost of the candies he bought from both Nash and Richard.

To find out how much Nash spent altogether,

First, let's calculate the cost of the candies Nash bought.

He bought 37 candies for 20 cents each.

So, the total cost of candies bought from Nash is

\(37 x 20 = 740 cents.\)

Next, let's calculate the cost of the candies Richard sold to Nash.

He sold 52 candies for 15 cents each.

So, the total cost of candies bought from Richard is

\(37 x 20 = 740 cents.\)
To find the total cost altogether,

we add the cost of candies bought from Nash and Richard.

\(740 cents + 780 cents = 1520 cents.\)
Since we need to express the answer in dollars,

we divide 1520 cents by 100 to convert it to dollars.

\(1520 cents / 100 = 15.20 dollars.\)

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Answer:

130

Step-by-step explanation:

since bc and bd equal the same thing, plug in every answer option until you get to 360.

(130 x 2) = 260

plus cd = 100.

260 + 100 = 360.

The arc length is twice the inscribed angle.

The sum of the three angles must be 180.

The measure of the arc length BC is 130°

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Triangle BCD is isosceles and BC ≅ BD.

Isosceles triangle C B D has points on the circle.

The measure of arc CD is 100 degrees.

This means,

We know that the arc length is twice the inscribed angle.

2 x Angle B = CD

2 x Angle B = 100

Angle B = 100/2

Angle B = 50

Now,

In an isosceles triangle, the angle opposite to the equal sides must be equal.

The sum of the three angles must be 180.

x + x + 50 = 180

2x = 180 - 150

2x = 130

x = 65

Now,

We know that the arc length is twice the inscribed angle.

So,

The measure of the arc length BC.

= 2 x 65

= 130°

Thus,

The measure of the arc length BC is 130°

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Yes, It is possible for two sets of data to have the same slope but different correlation coefficients depending on the direction of the relationship between the variables.

Two sets of data, Set A and Set B. Both sets have the same slope but different correlation coefficients.

Set A

x-values: [1, 2, 3, 4, 5]

y-values: [2, 4, 6, 8, 10]

Set B

x-values: [1, 2, 3, 4, 5]

y-values: [10, 8, 6, 4, 2]

For Set A, the points lie on a straight line that increases as x increases. The line has a positive slope, indicating a positive relationship between x and y. This positive relationship results in a high correlation coefficient, indicating a strong linear relationship between the variables.

For Set B, the points also lie on a straight line, but it decreases as x increases. The line has the same slope as Set A, indicating the same rate of change between x and y. However, the negative relationship between x and y in Set B leads to a negative correlation coefficient. This negative correlation coefficient indicates a strong linear relationship but in the opposite direction compared to Set A.

So, although both sets of data have the same slope, the difference in the direction of the relationship between x and y results in different correlation coefficients. Set A has a positive correlation coefficient, while Set B has a negative correlation coefficient.

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We prefer t procedures to z procedures for inference about a population mean because t procedures are more appropriate when the population standard deviation is unknown.

1. When the population standard deviation is known, we use z procedures. However, in many cases, the population standard deviation is not known and needs to be estimated from the sample data.
2. The t procedures take into account this uncertainty in estimating the population standard deviation by using the sample standard deviation in the calculations.
3. This makes the t procedures more accurate and reliable for inference about a population mean when the population standard deviation is unknown.

Therefore, t procedures are preferred over z procedures for inference about a population mean because they provide more accurate results when the population standard deviation is unknown.

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We can say with 95% confidence that the true mean percentage of water in the methanol solution falls between 0.528 and 0.566.

To find the 95% confidence interval for the percentage of water in the methanol solution, we first need to find the margin of error. This can be calculated as 1.96 times the standard deviation divided by the square root of the sample size, which in this case is 12.
Margin of error = 1.96 x (0.032 / sqrt(12)) = 0.019
Next, we can use the sample mean and the margin of error to construct the confidence interval
Confidence interval = sample mean +/- margin of error
Confidence interval = 0.547 +/- 0.019
Confidence interval = (0.528, 0.566)
Therefore, we can say with 95% confidence that the true mean percentage of water in the methanol solution falls between 0.528 and 0.566.
When we say that we are "95% confident" that the true mean u is in this interval, it means that if we were to repeat the same experiment multiple times and construct 95% confidence intervals each time, approximately 95% of those intervals would contain the true population mean. It is important to note that this does not mean that there is a 95% chance that the true mean falls within this specific interval – rather, either the true mean falls within this interval or it doesn't, and we have a 95% chance of constructing an interval that captures the true mean.

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Answer: 545.9

Step-by-step explanation:

637.1 - 91.2 = 545.9

Sorry that I couldn't explain more, but i hope this helps!

Also if it's right could you mark me as brainliest? I need 1 more to level up

The equation of the line is, y = -3x.

What is point slope form of the line?

A line's point slope form equation is y - y1 = m(x – x1). Consequently,

y - 0 = m(x - 0), or y = mx, is the equation of a line passing through the origin with a slope of m.

Let the line passes through the point (1, -3) and having slope of -3.

Consider, the point slope form of the line,

\(y-y_1=m(x-x_1)\)

Plug, \((x_1, y_1) = (1, -3), m = -3\)

So, the above equation becomes

\(y-(-3)=-3(x-1)\\y+3=-3x+3\\y=-3x+3-3\\y=-3x\)

Hence, the equation of line that passes through the point (1, -3) and having slope -3 is y = -3x.

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Answer:

Step-by-step explanation:

Answer:

50π or you can put 157

Step-by-step explanation:

So, the volume of a cone:

1/3*π*radius²*height

1/3π*25*6

50π

50*3.14 = 157

Answer:

5A)36 5b)30(mark as brainliest)

Step-by-step explanation:

5a)6+6+6+6+12 = 36

5b)36-8=28

28+2 = 30

Answer:

a: The answer is 36 units squared

b: You would lose four square units

Step-by-step explanation:

a: You can count the pieces showing, but you also have to add the amount you cannot see, which would give you a total of 36 units squared (since it doesn't say what each unit is represented by

b: The bottom pieces that originally were not showing would now be showing, but you would lose the ones above it. These cancel out from each other. There are 4 other sides that are now no longer showing since the others that are still showing still were anyways, so there are 4 units squared missing from the surface area when you remove the top two blocks.

The mean is just the multiplication of \(n\) and \(p\) so \(60 * 0.3\) = \(18\)

Variance is \((1 - p) * n * p\) so \(0.7 * 60 * 0.3 = 12.6\)

So the variance is \(12.6\)

The standard deviation is just the root of the variance so: \(\sqrt{12.6}\) = \(3.55\) rounded to the nearest hundredth. :D

Answer:

3/13 which is 0.23 as a decimal

Step-by-step explanation:

Answer:

y = 60

Step-by-step explanation:

"The ratio of y to x is 3"

This means that, \(y\div x=3\)

"The sum of y and x is 80"

This means,  \(x+y=80\)

If \(y\div x=3\), then \(y = (3*x)\).

We can plug this into the other equation by substitution:

\(x + (3 * x)=80\)

This simplifies to:

\(4x = 80\)

Which we can solve out and get:
\(x=20\).

We solved for x, but we need the value of y.

So, we go back to the equation we first derived: "\(y = (3*x)\)".

And now we substitute the value of x, into this.

\(y = (3 * (20))\)

By solving this out, we get:
\(y=60\)

So, the value of y is 60.

The probability that the first trial B, fails is given by 1-p. Hence, the correct answer is option C) 1-P.Let Y be a binomial random variable with parameters n and p.The probability that Y is zero is given by (1-p)^n. Hence, the correct answer is option A) (1-P)^n.

Bernoulli Distribution:In probability theory and statistics, the Bernoulli distribution is the discrete probability distribution of a random variable that takes the value 1 with probability p and the value 0 with probability q=1-p.

The Bernoulli distribution is the simplest distribution that has only two possible outcomes, 1 or 0.Binomial Distribution:The binomial distribution is a probability distribution that results from performing n independent Bernoulli trials, each with probability p of success.

A binomial random variable, Y, represents the number of successes in n Bernoulli trials with probability p.

The probability mass function of a binomial distribution is given byP(Y = k) = C(n, k) p^k q^(n-k)where C(n, k) = n!/[k! (n-k)!] is the binomial coefficient.P(Y = k) is the probability of getting k successes in n independent Bernoulli trials, where p is the probability of success in each trial and q = 1 - p is the probability of failure in each trial.

The question is formatted with HTML. Let B, and B, be Bernoulli trials with probability of success p.

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